A unifrom magnetic field B exists in a cylindrical region of radius 10 cm as shown in. A uniform wire of length 80 cm and resistance 4.0 Omega is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of 0.010 T/s, find the current induced in the frame.
(##HCV_VOL2_C38_E01_053_Q01##)

Options

A. `3.9xx10^(-5)A`
B. `4.0xx10^(5)A`
C. `4.1xx10^(-5)A`
D. `3.9xx10^(-4)A`

Answer

A

Explanation

Only half area of ring area of ring will be considered.
`therefore phi_(B)=BS=B.(pir^(2))/(2)`
`thereforee=(dphi_(B))/(dt)=(pir^(2))/(2).(dB)/(dt)=(pi(0.1)^(2))/(2)xx0.01=(pi)/(2)xx10^(-4)V`
`thereforei=(e)/(R)=((pi)/(2)xx10^(-4))/(4)=(pi)/(8)xx10^(-4)=3.9xx10^(-5)A`